From Basel Problem to multiple zeta values

TL;DR

This paper explores the implications of Boo Rim Choe's 1987 proof of the Basel problem for understanding multiple zeta values, using integral evaluations involving arcsine powers to connect various series and sums.

Contribution

It introduces new connections between the Basel problem proof and multiple zeta values through integral techniques involving arcsine functions.

Findings

Derived new identities relating binomial series and multiple zeta values

Established links between Basel problem solutions and multiple sums

Provided integral evaluations that simplify complex series

Abstract

We show many consequences of the proof of Basel problem by Boo Rim Choe (1987) to central binomial series, multiple zeta values and some other multiple sums. The main idea is to evaluate integrals involving powers of arcsine function.